EAGER-QAC-QSA: COLLABORATIVE RESEARCH: QUANTUM SIMULATION OF EXCITATIONS, BRAIDING, AND THE NONEQUILIBRIUM DYNAMICS OF FRACTIONAL QUANTUM HALL STATES

EAGER-QAC-QSA：合作研究：激发、编织和分数量子霍尔态的非平衡动力学的量子模拟

• 批准号: 2038028
• 负责人: Armin Rahmani
• 金额: $ 12.37万
• 依托单位: Western Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-09-15 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2038028&HistoricalAwards=false
• 关键词: EAGER; QAC; QSA; COLLABORATIVE; RESEARCH

NONTECHNICAL SUMMARYThis award supports theoretical research on the studies of dynamics of fractional quantum Hall states using a quantum computer. Recently, we have witnessed extensive development in building quantum computing devices. These advances have allowed efficient calculations of the properties of molecular systems of a few electrons, beyond the capabilities of classical computers. On the other hand, interactions among macroscopically large numbers of electrons lead to the emergence of novel states of matter such the fractional quantum Hall effect, which arises when electrons confined to two dimensions are placed in a strong magnetic field. Interestingly, it has been shown recently that there are connections between fractional quantum Hall states and quantum gravity. The understanding of these novel phenomena requires study of the quantum dynamics of many-particle states when driven out of equilibrium. Experimental and numerical investigations of such states are particularly challenging, motivating a completely new approach. The PIs will develop quantum algorithms to simulate and study these concepts using near-term quantum computing devices. This project will create a new table-top setup to explore questions ranging from quantum dynamics to gravity.The educational component of the activity will provide opportunities for undergraduate and graduate students, particularly from underrepresented groups, to learn about quantum computing and gain hands-on computational experience with quantum circuit design using Google's open-source packages.TECHNICAL SUMMARYThis award supports theoretical research on the nonequilibrium quench dynamics and the excitations of fractional quantum Hall states using superconducting qubits. Recent advances in quantum computing devices have motivated using them to simulate quantum states. Given the long-standing challenges in studying correlated many-electron phases, it is compelling to explore the possibility of using quantum computers to investigate these states. This project examines fractional quantum Hall states by developing efficient quantum algorithms that can be implemented on near-term quantum computers.Fractional quantum Hall states are significant examples of quantum phases, where topological order arises from strong electron-electron interactions. The understanding of fractional Hall states is primarily based on insightful trial wave functions, conformal field theory methods, exact diagonalization, and the density-matrix renormalization group. Despite extensive efforts, very little is known about the many-body excitation spectrum and the far-from-equilibrium dynamics of these systems. Notably, there has been a new understanding of novel geometric properties of fractional Hall states, which relates them to concepts in gravity. Advances in quantum computing and quantum simulations provide a new avenue to study fractional Hall phases out of equilibrium. In this research, the PIs pursue two particular directions:1- Quantum algorithms to generate dynamical quantum braiding and observe its signatures in fractional Hall phases. Even in natural quantum Hall systems, controlled generation of topological excitations and observation of quantum braiding have proved quite challenging. This project opens the door to using quantum computers as an experimental platform for realizing quantum braiding.2- Generating and observing signatures of geometric high-energy excitations, such as the putative emergent graviton in fractional quantum Hall states. To this end, the research utilizes the simulation of nonequilibrium geometric quenches of fractional Hall states on quantum computers.The PIs will use the network available at City College to involve high-school, undergraduate, and graduate students from underrepresented groups in the efforts to develop quantum algorithms. The PIs engage undergraduate students in this research, allowing them to gain authentic experience and independent research credit toward graduation. In particular, both PIs will use publicly available resources from Google AI lab to train the students in using software packages to design quantum algorithms and visualize them in terms of quantum gates.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术摘要这一奖项支持使用量子计算机对分数量子厅态动力学研究的理论研究。 最近，我们目睹了在构建量子计算设备方面的广泛发展。这些进步允许对几个电子的分子系统的性质有效计算，这是超出经典计算机功能的能力。另一方面，宏观上大量的电子之间的相互作用导致物质新颖状态的出现，例如分数量子霍尔效应，当将限制在二维的电子中时会出现。有趣的是，最近已经证明了分数量子霍尔状态与量子重力之间存在联系。对这些新现象的理解需要研究在平衡中驱动时许多粒子状态的量子动力学。对此类状态的实验和数值研究特别具有挑战性，激发了一种全新的方法。 PI将使用近期量子计算设备开发量子算法来模拟和研究这些概念。该项目将创建一个新的桌面设置，以探索从量子动态到重力的问题。该活动的教育成分将为本科生和研究生提供机会，特别是从代表性不足的小组中，学习量子计算，了解量子计算并获得量子的计算经验，并通过Google的开放式奖励进行量子研究，并获得了量子巡回演出。使用超导量子A的分数量子厅态的激发。量子计算设备的最新进展已激励使用它们模拟量子状态。 鉴于研究与多电子阶段相关的长期挑战，探索使用量子计算机研究这些状态的可能性是令人信服的。该项目通过开发可以在近期量子计算机上实现的有效量子算法来检查分数量子霍尔状态。截然量子霍尔状态是量子阶段的重要例子，其中拓扑顺序来自较强的电子电子相互作用。对分数霍尔状态的理解主要基于有见地的试验波函数，保形场理论方法，精确的对角线化和密度 - 矩阵的重生组。尽管进行了广泛的努力，但对这些系统的多体激发谱和远程平衡动力学知之甚少。值得注意的是，已经有了新的了解分数霍尔国家的新几何特性，这将它们与重力的概念有关。量子计算和量子模拟的进步为研究分数霍尔的阶段提供了新的途径。在这项研究中，PI追求两个特定的方向：1-量子算法以生成动力学量子编织，并在分数霍尔阶段观察其特征。即使在天然量子厅系统中，拓扑激发的受控产生和对量子编织的观察也很具有挑战性。 该项目为使用量子计算机作为实现量子编织的实验平台打开了大门。2-生成和观察几何高能激发的签名，例如分数量子霍尔的推定的新兴重力。为此，该研究利用了量子计算机上的分数大厅国家的非平衡几何淬灭的模拟。PIS将使用城市学院的网络来涉及高中，本科和来自代表性不足的群体的高中，本科生，以努力开发量子算法。 PI与本科生参与了这项研究，使他们能够获得真实的经验和独立的研究学分来毕业。特别是，这两个PI都将使用Google AI实验室的公开资源来培训学生使用软件包来设计量子算法并根据量子大门来可视化它们。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响审查标准来通过评估来通过评估来支持的。

项目成果

Braiding fractional quantum Hall quasiholes on a superconducting quantum processor

在超导量子处理器上编织分数量子霍尔准空穴

• DOI: 10.1103/physrevb.108.064303
• 发表时间: 2023
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Kirmani, Ammar;Wang, Derek S.;Ghaemi, Pouyan;Rahmani, Armin
• 通讯作者: Rahmani, Armin

Probing Geometric Excitations of Fractional Quantum Hall States on Quantum Computers

探测量子计算机上分数量子霍尔态的几何激发

• DOI: 10.1103/physrevlett.129.056801
• 发表时间: 2022
• 期刊: Physical Review Letters
• 影响因子: 8.6
• 作者: Kirmani, Ammar;Bull, Kieran;Hou, Chang-Yu;Saravanan, Vedika;Saeed, Samah Mohamed;Papić, Zlatko;Rahmani, Armin;Ghaemi, Pouyan
• 通讯作者: Ghaemi, Pouyan

Creating and Manipulating a Laughlin-Type ν=1/3 Fractional Quantum Hall State on a Quantum Computer with Linear Depth Circuits

在具有线性深度电路的量子计算机上创建和操纵 Laughlin 型 δ=1/3 分数量子霍尔态

• DOI: 10.1103/prxquantum.1.020309
• 发表时间: 2020
• 期刊: PRX Quantum
• 影响因子: 9.7
• 作者: Rahmani, Armin;Sung, Kevin J.;Putterman, Harald;Roushan, Pedram;Ghaemi, Pouyan;Jiang, Zhang
• 通讯作者: Jiang, Zhang